Recycle of random sequences

TL;DR

This paper investigates how permutation transformations affect the correlation of random sequences, demonstrating that shuffling can produce sequences nearly independent, with applications to Monte Carlo simulations, notably in Ising models.

Contribution

It introduces a method to analyze and reduce correlation in random sequences through permutation, enhancing Monte Carlo simulation accuracy.

Findings

Permutation can make sequences nearly independent

Shuffling reduces correlation significantly

Applicable to Ising Monte Carlo simulations

Abstract

The correlation between a random sequence and its transformed sequences is studied. In the case of a permutation operation or, in other word, the shuffling operation, it is shown that the correlation can be so small that the sequences can be regarded as independent random sequences. The applications to the Monte Carlo simulations are also given. This method is especially useful in the Ising Monte Carlo simulation.